The major challenge lies in the gap between the proposed problem setting and the conventional Empirical Risk Minimization (ERM) principle [1]}: the streaming data \(\mathcal {D}^t\)  lead to constant distribution shift. As non-stationary data distribution breaks the iid-sampled assumption, a learning solution is required to model the overall distribution of past observations without the need to store the entire dataset \(\mathcal {D}^{1:t}\) .
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